Question

A man bought a cow and a horse for $500. He sold the cow at a profit of 10% and the horse at a loss of 10% and suffered a loss of 2% on the whole. What did he pay for the cow?

Answer 1

The man paid $200 for the cow

Explanation:

System of Equations

Let's call:

x = price of the cow

y = price of the horse

The man bought the cow and the horse for $500, thus

x + y = 500 [1]

The cow was sold at a profit of 10%, thus:

Sale price of the cow= 1.1x

The horse was sold at a loss of 10%, thus:

Sale price of the horse= 0.9y

The total operation was a 2% loss, i.e. 0.98*500=490. Thus, we have:

1.1x + 0.9y = 490 [2]

From [1]:

y = 500 - x

Substituting in [2]:

1.1x + 0.9(500 - x) = 490

Operating:

1.1x + 450 - 0.9x = 490

0.2x = 490 - 450 = 40

x = 40/0.2

x = 200

The man paid $200 for the cow